That would definitely work, it's similar to how I do it. I don't have like the idea of having to control the temperature on the stove (I have quite an old stove with dialings 1, 2, 3, 4, 5 - 5 being the hottest setting so I have no idea how hot each can get to). I boil water in my jug and add it to a pot with 4 - 6 bottles then cover it with a towel to keep the steam in. Seems a bit primitive but it works fine, I let them sit for 10 - 15 minutes max and add some fresh boiling water at about 5 minutes. It works so well that I don't bother checking the temperature anymore, which is a bit foolish on my behalf.

Remember that your goal is to get the cider inside the bottles up to pasteurization temperature (e.g., 180 F) and keep it there for some length of time (20 minutes?).

I think the hard part will be figuring out how hot to make the water you add to the cooler to allow for how much it will cool down due to the cooler bottles. (Wow, I used "cool" a lot!)

What I mean is, if you want to hold the cider in the bottles at 180 F and the bottles start at room temperature (say 70F), you may need to add a few gallons of boiling hot water (212 F) to have the whole system come to rest at 180 (i.e., the cider temperature inside the bottles at 180). Will the bottles survive this kind of shock? I think you'd be better off putting the bottles in a stockpot with water and bringing the whole thing up to your desired temperature. If, at that point, you want to dump it all in a cooler, fine, but why bother?